A fast algorithm to calculate the dark channel prior (DCP) with the complexity constant for window size and linear for image size is presented. The strategy followed is that of ‘trade space for time’, and a data structure is developed, called the partitioned minimal table (PAMT), to orderly store the local minima of four partitions of every non‐overlapping patch. The comparisons of four values, one from each PAMT, give the DCP value at every pixel, which renders the fast DCP calculation. Experiments show that the fast algorithm greatly improves the time expense of DCP calculation where large size windows (hundreds) are necessary.